document.write( "Question 309769: The lengths of the sides of an isosceles triangle are 20, n, and n. If n is an integer, what is the smallest possible permiter of the triangle. Solution options are 40, 41, 42, 44, 60. Thank you. \n" ); document.write( "
Algebra.Com's Answer #221549 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The other tutor's solution is incorrect.\r\n" );
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document.write( "While it is true that the perimeter must be even, that\r\n" );
document.write( "is not enough information.\r\n" );
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document.write( "The sides are 20, n, and n.\r\n" );
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document.write( "Every triangle must be such that\r\n" );
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document.write( "(its first side) + (its second side) > (its third side)\r\n" );
document.write( "(its first side) + (its third side) > (its second side)\r\n" );
document.write( "(its second side) + (its third side) > (its first side)\r\n" );
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document.write( "Let its first side = 20, its second side be n and its third side be n\r\n" );
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document.write( "Then we must have:\r\n" );
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document.write( "20 + n > n\r\n" );
document.write( "20 + n > n\r\n" );
document.write( "n + n > 20\r\n" );
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document.write( "or\r\n" );
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document.write( "20 > 0\r\n" );
document.write( "20 > 0\r\n" );
document.write( "2n > 20\r\n" );
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document.write( "The first two inequalities are always true, and\r\n" );
document.write( "the last inequality\r\n" );
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document.write( "2n > 20\r\n" );
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document.write( "is true whenever\r\n" );
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document.write( "n > 10\r\n" );
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document.write( "The smallest integer n could be such that n > 10 is n = 11\r\n" );
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document.write( "So the sides of the triangle with smallest possible perimeter\r\n" );
document.write( "are 20, 11 and 11, so the smallest perimeter is \r\n" );
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document.write( "20+11+11=42\r\n" );
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document.write( "Edwin
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